利用模糊理論和層級分析法解排班問題

Applying Fuzzy and AHP toSolve Nurse Scheduling Problems

林英傑(Ying-Jie Lin)

指導教授 ： 陳平舜

中原大學/電機資訊學院/工業與系統工程研究所/碩士(2013年)

https://doi.org/10.6840/cycu201300883

摘要

醫事放射師的排班問題為一多目標規劃問題。本研究的研究目的是為了求得適當的醫事放射師人數，並在滿足政府法規、醫院規定和護理人員偏好等限制下產生班表。醫事放射師的排班是採用一個星期七天，每天三班，每班8小時的輪班制。本研究不僅有相關規定之硬限制(舉例：政府法規)，也加入軟限制(舉例：護理人員偏好)，讓這個複雜的排班問題可以更加靈活且實用。
本研究的研究方法是利用模糊理論，求出班表適合的醫事放射師人數；其次，建立醫事放射師的多目標排班問題；最後，採用層級分析法，計算多目標權重，並利用ILOG軟體求出最佳解。目標式為0時，表示有不違反軟限制之解；目標式大於0時，則表示有至少違反一個軟性限制之解。此外，本研究在醫事放射師的人數進行敏感度分析，結果證明醫院能夠確定可行的醫事放射師人數，並取得班表。本研究最後進行情境分析，探討加入休假限制對醫事放射師班表的影響，結果發現增加休假限制可以產生一個更公平的醫事放射師班表。

關鍵字

層級分析法 ； 模糊理論 ； 整數規劃 ； 多目標規劃、護理排班

並列摘要

The radiologist scheduling problem is a multi-objective and complicated problem. The purpose of this research is to obtain an appropriate number of radiologists, and assign their monthly schedule which satisfies the government regulations, hospital regulations, and the radiologists’ preference. The radiologists of the Emergency Room have eight hour a shift, three shifts a day,and seven days a week. This research considers not only hard constraints (i.e., government regulation), but also soft constraints (i.e., radiologists’ preference). Hence, the formulated radiologist scheduling problem becomes more flexible and practical.
The methodology of this research is to use the fuzzy theory to obtain the appropriate radiologists, construct a multi-objective radiologist scheduling problem, and apply the analytic hierarchy process (AHP) to determine the weight of objectives. This study adopts the ILOG software to solve this proposed problem. If the optimal solution is zero, it means that there is no violation against soft constraints. Otherwise, there is at least one violation against soft constraints.
Further, this research performs the sensitivity analysis for the number of radiologists. The findings show that hospitals can determine the feasible number of radiologists and obtain their monthly schedule. This study performs the scenario analysis to explore the impact of the vacation constraint on the radiologist schedule. The outcomes show that adding the vacation constraint can generate a fairer radiologist schedule.

並列關鍵字

Integer programming ； Multi-objective programming ； Nurse scheduling ； Fuzzy theory ； Analytic hierarchy process (AHP)

參考文獻

林廷臻，隸屬度函數及區間長度改良對模糊時間序列預測之影響探討，大同大學應用數學研究所碩士論文，2008。

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